A tutorial on graph models for scheduling round-robin sports tournaments

Many sports leagues organize their competitions as round-robin tournaments. This tournament design has a rich mathematical structure that has been studied in the literature over the years. We review some of the main properties and fundamental scheduling methods of round-robin tournaments. Special attention is given to extra-mural tournaments in which each team in the competition has its venue. Teams play either at home or away in such tournaments in each round. The surge of breaks in the perfect alternation of home and away breaks is studied in detail.